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On the convergence of stochastic transport equations to a deterministic parabolic one
Lucio Galeati · 2019-02-19 · via math.PR updates on arXiv.org

A stochastic transport linear equation (STLE) with multiplicative space-time dependent noise is studied. It is shown that, under suitable assumptions on the noise, a multiplicative renormalization leads to convergence of the solutions of STLE to the solution of a deterministic parabolic equation. Existence and uniqueness for STLE are also discussed. Our method works in dimension $d\geq 2$; the case $d=1$ is also investigated but no conclusive answer is obtained.

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